Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry

Recently, there has been rapid progress in classifying topological band structures by examining possible configurations, arising through consideration of the constraints of the underlying lattice symmetry. Apart from topologically stable and trivial bands, these pursuits have identified fragile topologies that can be trivialized by additional bands. The authors present a general and directly implementable tool to diagnose the full topological characterization of bands using Wilson flows. As a result, they find a general relation and unambiguous representation of these novel topological concepts.